Sudden jumps and plateaus in the quench dynamics of a Bloch state (original) (raw)

Take a one-dimensional tight binding chain with the periodic boundary condition and put a particle in some Bloch state, then quench it by suddenly changing the potential of some site. In the ensuing time evolution, the probability density of the wave function at an arbitrary site jumps constantly between plateaus. This phenomenon adds to another one that the survival probability of the particle in the initial Bloch state shows cusps periodically, which was found previously in the same scenario (Zhang and Yang, arXiv:1601.03569). The two, one in the real space and one in the momentum space, complement each other to provide a comprehensive picture of the quench dynamics of a Bloch state. Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of a fictitious model, based on which, the locations of the jumps and the heights of the plateaus are accurately predicted.

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